Hopf Algebras in Group Yetter-Drinfel＇d Categories

摘要

In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category LLYD(π) over a crossed Hopf group-coalgebra L, then its dual H is also a Hopf algebra in the category LLYD(π). Then we establish the fundamental theorem of Hopf modules for H in the category LLYD(π).